# A regular polygon has an exterior angle measure of (x+3) degrees and an interior angle measure of (13x - 33) degrees. # of sides polygon has is? Need to know the: 1. Measure of each angle in the polygon 2. How many sides does this polygon have? Please show work.  We could not figure it out. A regular polygon has an exterior angle measure of `x+3` degrees, and an interior angle measure of `13x-33` degrees. Find the number of sides.

(1) The exterior and interior angles at a vertex are supplementary, thus

`13x-33+x+3=180` `14x=210` `x=15`

(2) Then the exterior angle of the polygon is `18^circ` ....

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A regular polygon has an exterior angle measure of `x+3` degrees, and an interior angle measure of `13x-33` degrees. Find the number of sides.

(1) The exterior and interior angles at a vertex are supplementary, thus

`13x-33+x+3=180`
`14x=210`
`x=15`

(2) Then the exterior angle of the polygon is `18^circ` . (The interior angle is `162^circ` ). Since the polygon is regular, all interior angles are equal, as are each of the exterior angles.

(3) The sum of the exterior angles of any polygon (taken one at each vertex) is `360^circ` . Since all the exterior angles are congruent, the number of sides is `(360)/(18)=20` .

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